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作者：Hoshino, Masato; Kawabi, Hiroshi; Kusuoka, Seiichiro
作者单位：University of Osaka; Keio University; Kyoto University
摘要：The present paper is a continuation of our previous work (Hoshino et al., J Evol Equ 21:339-375,2021) on the stochastic quantization of the exp(Phi)(2)-quantum field model on the two-dimensional torus. Making use of key properties of Gaussian multiplicative chaos and refining the method for singular SPDEs introduced in the previous work, we construct a unique time-global solution to the corresponding parabolic stochastic quantization equation in the full L-1 -regime vertical bar alpha vertical...
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作者：Hall, Brian C.; Ho, Ching-Wei
作者单位：University of Notre Dame; Academia Sinica - Taiwan
摘要：We consider a family of free multiplicative Brownian motions b(s,tau) parametrized by a real variance parameter s and a complex covariance parameter tau. We compute the Brown measure mu(s,r) of ub(s,tau) where u is a unitary element freely independent of b(s,tau). We find that mu(s,r) has a simple structure, with a density in logarithmic coordinates that is constant in the tau-direction. These results generalize those of Driver-Hall-Kemp and Ho-Thong for the case tau = s. We also establish a r...
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作者：Basak, Anirban
作者单位：Tata Institute of Fundamental Research (TIFR); International Centre for Theoretical Sciences, Bengaluru
摘要：We consider an Erdos-Renyi graph G(n, p) on n vertices with edge probability p such that log n log log n np n1/2-o(1), () and derive the upper tail large deviations of.(G(n, p)), the largest eigenvalue of its adjacency matrix. Within this regime we show that, for p n -2/3 the log-probability of the upper tail event of.(G(n, p)) equals to that of planting a clique of an appropriate size (upon ignoring smaller order terms), while for p n -2/3 the same is given by that of the existence of a high ...
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作者：Regts, Guus
作者单位：University of Amsterdam
摘要：In this paper we show that absence of complex zeros of the partition function of the hard-core model on any family of bounded degree graphs that is closed under taking induced subgraphs implies that the associated probability measure, the hard-core measure, satisfies strong spatial mixing on that family. As a corollary we obtain that the hard-core measure on the family of bounded degree claw-free graphs satisfies strong spatial mixing for every value of the fugacity parameter. We furthermore d...
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作者：Damron, Michael; Hanson, Jack; Harper, David; Lam, Wai-Kit
作者单位：University System of Georgia; Georgia Institute of Technology; City University of New York (CUNY) System; City College of New York (CUNY); National Taiwan University; University of Minnesota System; University of Minnesota Twin Cities
摘要：In first-passage percolation (FPP), we let(tau(v))be i.i.d. nonnegative weights on thevertices of a graph and study the weight of the minimal path between distant vertices. If Fi s the distribution function of tau v, there are different regimes: if F(0) is small,this weight typically grows like a linear function of the distance, and when F(0) islarge, the weight is typically of order one. In between these is the critical regime inwhich the weight can diverge, but does so sublinearly. We study ...
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作者：Kolliopoulos, Nikolaos; Larsson, Martin; Zhang, Zeyu
作者单位：Carnegie Mellon University
摘要：We study the asymptotic behavior of the normalized maxima of real-valued diffusive particles with mean-field drift interaction. Our main result establishes propagation of chaos: in the large population limit, the normalized maxima behave as those arising in an i.i.d. system where each particle follows the associated McKean-Vlasov limiting dynamics. Because the maximum depends on all particles, our result does not follow from classical propagation of chaos, where convergence to an i.i.d. limit ...
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作者：Angel, Omer; Ray, Gourab; Spinka, Yinon
作者单位：University of British Columbia; University of Victoria; Tel Aviv University
摘要：From each point of a Poisson point process start growing a balloon at rate 1. When two balloons touch, they pop and disappear. Is every point contained in balloons infinitely often or not? We answer this for the Euclidean space, the hyperbolic plane and regular trees. The result for the Euclidean space relies on a novel 0-1 law for stationary processes. Towards establishing the results for the hyperbolic plane and regular trees, we prove an upper bound on the density of any well-separated set ...
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作者：Huesmann, Martin; Mattesini, Francesco; Otto, Felix
作者单位：University of Munster; Max Planck Society
摘要：We show that there is no cyclically monotone stationary matching of two independent Poisson processes in dimension d = 2. The proof combines the harmonic approximation result from Goldman et al. (Commun. Pure Appl. Math. 74:2483-2560, 2021) with local asymptotics for the two-dimensional matching problem for which we give a new self-contained proof using martingale arguments.
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作者：Ding, Jian; Liu, Haoyu
作者单位：Peking University
摘要：We study the shotgun assembly problem for the lattice labeling model, where i.i.d. uniform labels are assigned to each vertex in a d-dimensional box of side length n. We wish to recover the labeling configuration on the whole box given empirical profile of labeling configurations on all boxes of side length r. We determine the threshold around which there is a sharp transition from impossible to recover with probability tending to 1, to possible to recover with an efficient algorithm with prob...
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作者：Lacker, Daniel; Le Flem, Luc
作者单位：Columbia University
摘要：We prove the optimal rate of quantitative propagation of chaos, uniformly in time, for interacting diffusions. Our main examples are interactions governed by convex potentials and models on the torus with small interactions. We show that the distance between the k-particle marginal of the n-particle system and its limiting product measure is O((k/n)(2)), uniformly in time, with distance measured either by relative entropy, squared quadratic Wasserstein metric, or squared total variation. Our p...
